Emergent O(<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math>) symmetry in a series of three-dimensional Potts models

Ding, Chengxiang; Blöte, Henk W. J.; Deng, Youjin

doi:10.1103/physrevb.94.104402

Cited by 18 publications

(18 citation statements)

References 35 publications

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“…In this paper we will show the details and steps that have been been used to perform the continuum extrapolation. A similar analysis for light quarks can be found in [17,18].…”

Section: Introductionsupporting

confidence: 61%

Continuum extrapolation of quarkonium correlators at non-zero temperature

et al. 2018

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In the investigation of in-medium modifications of quarkonia and for determining heavy quark diffusion coefficients, correlation functions play a crucial role. For the first time we perform a continuum extrapolation of charmonium and bottomonium correlators in the vector channel based on non-perturbatively clover-improved Wilson fermions in quenched lattice QCD. Calculations were done at 4 different lattice spacings, spatial extents between 96 and 192, aspect ratio from 1/6 to 1/2, for 5 temperatures between T/T c = 0.75 and T/T c = 2.2. We interpolate between different quark masses to match to the same vector meson mass over different lattice setups. Afterwards we extrapolate the renormalized correlators to the continuum. While we find a strong temperature dependence for charmonium, bottomonium states are only slightly affected at higher temperatures.Speaker,

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“…In this paper we will show the details and steps that have been been used to perform the continuum extrapolation. A similar analysis for light quarks can be found in [17,18].…”

Section: Introductionsupporting

confidence: 61%

Continuum extrapolation of quarkonium correlators at non-zero temperature

et al. 2018

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“…1 we plot the variation of this approximant versus one of the numerator parameters while the other seven parameters are determined from the seven coefficients in Eq. (19)…”

Section: Error Calculationsmentioning

confidence: 99%

“…For the study of critical phenomena in the O(N ) vector model, Monte Carlo simulations have been used successfully and give precise results for the critical exponents [12][13][14][15][16][17][18][19][20][21]. Besides, bootstrapping the model in three dimensions has been accomplished recently and researchers succeeded to obtain precise results [22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Critical exponents of the O(N)-symmetric $$\phi ^4$$ model from the $$\varepsilon ^7$$ hypergeometric-Meijer resummation

Shalaby

2021

Eur. Phys. J. C

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We extract the $$\varepsilon $$ ε -expansion from the recently obtained seven-loop g-expansion for the renormalization group functions of the O(N)-symmetric model. The different series obtained for the critical exponents $$\nu ,\ \omega $$ ν , ω and $$\eta $$ η have been resummed using our recently introduced hypergeometric-Meijer resummation algorithm. In three dimensions, very precise results have been obtained for all the critical exponents for $$N=0,1,2,3$$ N = 0 , 1 , 2 , 3 and 4. To shed light on the obvious improvement of the predictions at this order, we obtained the divergence of the specific heat critical exponent $$\alpha $$ α for the XY model. We found the result $$-0.0123(11)$$ - 0.0123 ( 11 ) which is compatible with the famous experimental result of $$-0.0127(3)$$ - 0.0127 ( 3 ) from the specific heat of zero gravity liquid helium superfluid transition while the six-loop Borel with conformal mapping resummation result in literature gives the value $$-0.007(3)$$ - 0.007 ( 3 ) . For the challenging case of resummation of the $$\varepsilon $$ ε -expansion series in two dimensions, we showed that our resummation results reflect a significant improvement to the previous six-loop resummation predictions.

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“…In the by now canonical papers [19,20], for the 2D TFFIM on the triangle lattice, as a function of magnetic field, the QCP between the magnetically ordered clock phase and the fully polarized phase are shown by both LGW renormalization group analysis and unbiased Monte Carlo (MC) simulations to be of the (2 + 1)D O(2) universality class, despite the original Hamiltonian only contains discrete Ising symmetry. In a broader sense, emergent O(n) symmetries have also been observed in the classical (finite temperature) transition in 3D q-state Potts model [21], and in 2D, a QCP with an emergent U (1) symmetry is the prominent feature of the famous deconfined quantum-critical point [22,23], which separates antiferromagnetic Néel state and valence-bondsolid [24? , 25].…”

Section: Introductionmentioning

confidence: 99%

Caution on emergent continuous symmetry: A Monte Carlo investigation of the transverse-field frustrated Ising model on the triangular and honeycomb lattices

Wang

Chen

et al. 2017

Phys. Rev. B

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Continuous symmetries are believed to emerge at many quantum critical points in frustrated magnets. In this work, we study two candidates of this paradigm: the transverse-field frustrated Ising model (TFFIM) on the triangular and the honeycomb lattices. The former is the prototypical example of this paradigm, and the latter has recently been proposed as another realization. Our large-scale Monte Carlo simulation confirms that the quantum phase transition (QPT) in the triangular lattice TFFIM indeed hosts an emergent O(2) symmetry, but that in the honeycomb lattice TFFIM is a first-order QPT and does not have an emergent continuous symmetry. Furthermore, our analysis of the order-parameter histogram reveals that such different behavior originates from the irrelevance and relevance of anisotropic terms near the QPT in the low-energy effective theory of the two models. The comparison between theoretical analysis and numerical simulation in this work paves the way for scrutinizing investigation of emergent continuous symmetry at classical and quantum phase transitions.

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Emergent O(n) symmetry in a series of three-dimensional Potts models

Cited by 18 publications

References 35 publications

Continuum extrapolation of quarkonium correlators at non-zero temperature

Continuum extrapolation of quarkonium correlators at non-zero temperature

Critical exponents of the O(N)-symmetric $$\phi ^4$$ model from the $$\varepsilon ^7$$ hypergeometric-Meijer resummation

Caution on emergent continuous symmetry: A Monte Carlo investigation of the transverse-field frustrated Ising model on the triangular and honeycomb lattices

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